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A ClosedForm Solution for Mapping General Distributions to Minimal PH Distributions
 In Performance TOOLS
, 2003
"... Approximating general distributions by phasetype (PH) distributions is a popular technique in queueing analysis, since the Markovian property of PH distributions often allows analytical tractability. ..."
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Cited by 26 (14 self)
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Approximating general distributions by phasetype (PH) distributions is a popular technique in queueing analysis, since the Markovian property of PH distributions often allows analytical tractability.
A closed form solution for mapping general distributions to minimal ph distributions
 In International Conference on Performance Tools – TOOLS 2003
, 2003
"... Approximating general distributions by phasetype (PH) distributions is a popular technique in stochastic analysis, since the Markovian property of PH distributions often allows analytical tractability. This paper proposes an algorithm for mapping a general distribution, G, to a PH distribution, whi ..."
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Cited by 19 (1 self)
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Approximating general distributions by phasetype (PH) distributions is a popular technique in stochastic analysis, since the Markovian property of PH distributions often allows analytical tractability. This paper proposes an algorithm for mapping a general distribution, G, to a PH distribution, which matches the first three moments of G. Efficiency of our algorithm hinges on narrowing the search space to a particular subset of the PH distributions, which we refer to as EC distributions. The class of EC distributions has a small number of parameters, and we provide closedform solutions for these. Our solution applies to any distribution whose first three moments can be matched by a PH distribution. Also, our resulting EC distribution requires a nearly minimal number of phases, within one of the minimal number of phases required by any acyclic PH distribution. Key words: PH distribution, moment matching, closed form, normalized moment PACS: 1
Application of Network Calculus to General Topologies Using TurnProhibition
 IEEE/ACM Transactions on Networking
, 2002
"... Network calculus is known to apply in general only to feedforward routing networks, i.e., networks where routes do not create cycles of interdependent packet flows. In this paper, we address the problem of using network calculus in networks of arbitrary topology. For this purpose, we introduce a no ..."
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Cited by 18 (3 self)
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Network calculus is known to apply in general only to feedforward routing networks, i.e., networks where routes do not create cycles of interdependent packet flows. In this paper, we address the problem of using network calculus in networks of arbitrary topology. For this purpose, we introduce a novel graphtheoretic algorithm, called turnprohibition (TP), that breaks all the cycles in a network and, thus, prevents any interdependence between flows. We prove that the TPalgorithm prohibits the use of at most 1/3 of the total number turns in a network, for any network topology. Using analysis and simulation, we show that the TPalgorithm significantly outperforms other approaches for breaking cycles, such as the spanning tree and up/down routing algorithms, in terms of network utilization and delay bounds. Our simulation results also show that the network utilization achieved with the TPalgorithm is within a factor of two of the maximum theoretical network utilization, for networks of up to 50 nodes of degree four. Thus, in many practical cases, the restriction of network calculus to feedforward routing networks may not represent a too significant limitation.
Scheduling flows with unknown sizes: Approximate analysis
, 2002
"... Abstract Previous studies have shown that giving preferential treatment to short jobs helps reduce the average system response time, especially when the job size distribution possesses the heavytailed (HT) property. Since it has been shown that the TCP flow length distribution also has the same prop ..."
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Cited by 17 (1 self)
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Abstract Previous studies have shown that giving preferential treatment to short jobs helps reduce the average system response time, especially when the job size distribution possesses the heavytailed (HT) property. Since it has been shown that the TCP flow length distribution also has the same property, it is natural to let short TCP flows enjoy better service inside the network. Analyzing such discriminatory system requires modification to traditional job scheduling models since usually network traffic managers do not have detailed knowledge about individual flows such as their lengths. The MultiLevel queue, proposed by Kleinrock, can be used to to characterize such system. In this paper, we perform an approximate analysis on the MultiLevel queueing system to obtain closedform solution of the average system response time function. 1 Introduction Previous job scheduling studies indicate that providing rapid response to interactive jobs which place frequent but small demands, can reduce the overall system average response time [1]. Such sizeaware discriminatory scheduling algorithms have been shown, both experimentally and analytically (see [2] and references therein), to work extremely well when the job size distribution possesses the heavytailed (HT) property1. Since data transfer in a network can be modeled as a flow scheduling problem, and the HT property has been observed in the length of Internet transactions, especially Web file transfers, it is natural to design a network system that favors short file transfers.
Necessary and sufficient conditions for representing general distributions by Coxians
 In Proceedings of TOOLS '03
, 2002
"... A common analytical technique involves using a Coxian distribution to model a general distribution G, where the Coxian distribution agrees with G on the rst three moments. This technique is motivated by the analytical tractability of the Coxian distribution. Algorithms for mapping an input distribu ..."
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Cited by 8 (4 self)
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A common analytical technique involves using a Coxian distribution to model a general distribution G, where the Coxian distribution agrees with G on the rst three moments. This technique is motivated by the analytical tractability of the Coxian distribution. Algorithms for mapping an input distribution G to a Coxian distribution largely hinge on knowing a priori the necessary and sucient number of phases in the representative Coxian distribution. In this paper, we formally characterize the set of distributions G which are wellrepresented by an nphase Coxian distribution, in the sense that the Coxian distribution matches the rst three moments of G. We also discuss a few common, practical examples.
Analysis of multiserver systems via dimensionality reduction of Markov chains
 School of Computer Science, Carnegie Mellon University
, 2005
"... The performance analysis of multiserver systems is notoriously hard, especially when the system involves resource sharing or prioritization. We provide two new analytical tools for the performance analysis of multiserver systems: moment matching algorithms and dimensionality reduction of Markov chai ..."
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Cited by 7 (4 self)
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The performance analysis of multiserver systems is notoriously hard, especially when the system involves resource sharing or prioritization. We provide two new analytical tools for the performance analysis of multiserver systems: moment matching algorithms and dimensionality reduction of Markov chains (DR). Moment matching algorithms allow us to approximate a general distribution with a phase type (PH) distribution. Our moment matching algorithms improve upon existing ones with respect to the computational efficiency (we provide closed form solutions) as well as the quality and generality of the solution (the first three moments of almost any nonnegative distribution are matched). Approximating job size and interarrival time distributions by PH distributions enables modeling a multiserver system by a Markov chain, so that the performance of the system is given by analyzing the Markov chain. However, when the multiserver system involves resource sharing or prioritization, the Markov chain often has a multidimensionally infinite state space, which makes the analysis computationally hard. DR allows us to closely approximate a multidimensionally infinite Markov chain with a Markov
Performance of server selection algorithms for content replication networks
 In NETWORKING 2005
, 2005
"... Abstract. In this paper, we investigate the problem of optimal server selection in “content replication networks, ” such as peertopeer (P2P) and content delivery networks (CDNs). While a number of server selection policies have been proposed or implemented, understanding of the theoretical perform ..."
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Cited by 3 (0 self)
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Abstract. In this paper, we investigate the problem of optimal server selection in “content replication networks, ” such as peertopeer (P2P) and content delivery networks (CDNs). While a number of server selection policies have been proposed or implemented, understanding of the theoretical performance limits of server selection and the relative performance of existing policies remains limited. In this paper, we introduce a mathematical framework, based on the M/G/1 Processor Sharing queueing model, and derive closedform expressions for the optimal server access probabilities and the optimal average delay. We also analyze the performance of two general server selection policies, referred to as EQ DELAY and EQ LOAD, that characterize a wide range of existing algorithms. We prove that the average delay achieved by these policies can theoretically be as much as N times larger than the optimal delay, where N is the total number of servers in the system. Furthermore, simulation results obtained using our M/G/1PS workload model and the ProWGen Web workload generator show that the optimal policy can reduce the average delay of requests by as much as 30 % as compared to EQ LOAD and EQ DELAY, in realistic scenarios. They also show that the optimal policy compares favorably to the other policies in terms of fairness and sensitivity to traffic parameters. 1
Stochastic Models for Web Servers
, 2005
"... Hagit, there are so many things that I want to thank you for. You always left your door open for me. You always welcomed me with a big smile and endless patience. With one hand, you gave me academic freedom to choose the subjects and with the other hand you escorted, supported and guided me. How can ..."
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Hagit, there are so many things that I want to thank you for. You always left your door open for me. You always welcomed me with a big smile and endless patience. With one hand, you gave me academic freedom to choose the subjects and with the other hand you escorted, supported and guided me. How can I thank you for the infinite time you spent reading, commenting, and improving this research? In fact, you where the one who taught me what the meaning of an academic research is. I would like to thank Hadas Shachnai, whom I used to bother asking her to referee and discuss most of the results reached in this thesis. She was always kind and her comments were always relevant and helped me to improve the research. The final exam was conducted by Hagit, Hadas and Yuval Shavit in both a friendly atmosphere and on high intellectual level. Thank you. In the beginning of my research I had some useful discussions with Roy Friedman, Danny Raz and Roman Vitenberg which widened my horizons. I would like to thank my family for their support. My mother, Dina Teplixke, who could not care less about my grades except for the one in mathematics... My husband, Nir, who
Inference of Link Delay through Measurement Redundancy in Communication Networks
"... This paper studies the feasibility and algorithms for inferring delay at each link in a communication network based on a large number of endtoend measurements. The restriction is that we are not allowed to measure directly on each link and can only observe the total delays on one or more network r ..."
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This paper studies the feasibility and algorithms for inferring delay at each link in a communication network based on a large number of endtoend measurements. The restriction is that we are not allowed to measure directly on each link and can only observe the total delays on one or more network routes that include that link. It is assumed that we have considerable flexibility in choosing which route to measure. We investigate three different cases: (1) each link delay is a constant; (2) each link delay is modeled as a random variable from a family of distributions with unknown parameters; and (3) each link delay is a random variable whose distribution is completely unknown. We will answer whether such indirect measurement is possible at all, and when possible, how such measurement can be carried out.
Handoff Counting in Hierarchical Cellular System With Overflow Scheme
, 2004
"... InmobiT computi: scenarik the number of hando# (called as hando# counting)i s veryirypkxfik for thesi#TxI)p: networkdesir and tra#c loadanalysi( Inthi paper, we study the hando#countik characterip:k( i terms of probabip:k massfunctix (pmf) and statij(p:) momentsi thehi)x(jp:)fi cellular systemapp ..."
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InmobiT computi: scenarik the number of hando# (called as hando# counting)i s veryirypkxfik for thesi#TxI)p: networkdesir and tra#c loadanalysi( Inthi paper, we study the hando#countik characterip:k( i terms of probabip:k massfunctix (pmf) and statij(p:) momentsi thehi)x(jp:)fi cellular systemapplyik overflow scheme under the general cellresi()## tii and general callholdi# tid dii##Ikp:)x The analytip: result and thealgorijI for the evaluati) of hando#counti( are,respectip:)j presented for the cases whether or not theLaplaceStij#pi Transform of callholdi( tid exii( Thenumeri)fi results reveal that as the callholdi tid i heavytai:) the hando#countij follows theheavytai)T tendency. Inaddi(Ip the hando#countik pmf as well as the average value shows a si)Tp:)## di)Tp:) patternwit theuti(T(#p:) ofdi)xIk callholdi( tid dii(xxIp:)# # 2004ElseviI B.V. Allrip(# reserved.